Method for drying thin films in an energy efficient manner

ABSTRACT

A method for drying a thin film stack having a thin film located on a substrate is disclosed. The thin film stack is conveyed past a flashlamp during which the thin film stack is irradiated with a composite light pulse from the flashlamp. The composite light pulse is composed of multiple micropulses. The time duration of the composite light pulse is shorter than a total thermal equilibration time of the thin film stack. In addition, when the thin film stack is being conveyed past the flashlamp, the thin film stack should move less than 10% of the length of the irradiating area in the conveyance direction during the delivery of the composite light pulse.

PRIORITY CLAIM

The present application is a continuation-in-part of U.S. patentapplication Ser. No. 13/082,469, filed on Apr. 8, 2011, now U.S. Pat.No. 8,907,258 the contents of which are incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates to thermally processing thin films ingeneral, and, in particular, to a method for drying thin films by usinglight pulses from a flashlamp.

2. Description of Related Art

When it comes to choosing substrates for supporting thin films, it isgenerally more preferable to employ inexpensive substrates, such aspolyethylene terephthalate (PET), polycarbonate, cellulose, etc., overexpensive substrates, such as silicones, fluorocarbons, ceramic, glass,etc., due to cost reasons. However, inexpensive substrates tend to havelower maximum working temperatures than their expensive counterpartssuch that only relatively low temperatures can be utilized to dry thinfilms located on inexpensive substrates.

According to the Arrhenius equation, thermally driven processes, such asdrying (i.e., driving off solvent), particle sintering, densification,chemical reaction initiation, chemical reaction modulation, phasetransformation, grain growth, annealing, heat treating, etc., arerelated to the processing temperature in an exponential fashion. Hence,a small reduction in the drying temperature will require a significantlylonger drying time and more energy, which translates to a more costlydrying operation.

Consequently, it would be desirable to provide an improved process forthermally processing thin films located on inexpensive substrateswithout extending the processing time.

SUMMARY OF THE INVENTION

In accordance with a preferred embodiment of the present invention, athin film stack is thermally processed by conveying the thin film stackpast a flashlamp during which the thin film stack is irradiated with acomposite light pulse from the flashlamp. The composite light pulse iscomposed of multiple micropulses. The time duration of the compositelight pulse is shorter than a total thermal equilibration time of thethin film stack. In addition, when the thin film stack is being conveyedpast the flashlamp, the thin film stack should move less than 10% of thelength of the irradiating area in the conveyance direction during thedelivery of the composite light pulse.

All features and advantages of the present invention will becomeapparent in the following detailed written description.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention itself, as well as a preferred mode of use, furtherobjects, and advantages thereof, will best be understood by reference tothe following detailed description of an illustrative embodiment whenread in conjunction with the accompanying drawings, wherein:

FIG. 1 is a diagram of a thin film stack;

FIG. 2a shows the intensity and pulse length of a single light pulse anda composite light pulse, each can be used for heating the thin filmstack from FIG. 1;

FIG. 2b is a graph showing the temperature of a substrate versus timeafter the substrate has been irradiated by the single light pulse fromFIG. 2 a;

FIG. 2c is a graph showing the temperature of a substrate versus timeafter the substrate has been irradiated by the composite light pulsefrom FIG. 2 a;

FIG. 2d is a composite light pulse capable of providing two differentconstant processing temperature zones;

FIG. 2e is a graph showing the temperature of a substrate versus timeafter the substrate has been irradiated by the composite light pulsefrom FIG. 2 d;

FIG. 3 is a diagram of a drying apparatus for generating the compositelight pulse from FIG. 2a , in accordance with a preferred embodiment ofthe present invention; and

FIG. 4 is a block diagram of a flashlamp controller within the dryingapparatus from FIG. 3.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

A. Thermal Equilibration Time of a Thin Film Stack

The thermal equilibrium time τ of a layer of material is calculated by:

$\tau = \frac{c\; p\; x^{2}}{4\;\kappa}$

-   -   where c=specific heat of the material        -   ρ=mass density of the material        -   x=thickness of the material        -   κ=thermal conductivity of the material

The total thermal equilibration time τ_(stack) for a thin film stackhaving multiple layers of different materials with different thicknessescan be calculated by:τ_(stack)=(√{square root over (τ₁)}+√{square root over (τ₂)}+√{squareroot over (τ₃)} . . . √{square root over (τ_(i))})²where τ₁, τ₂, τ₃, etc. are the thermal equilibrium time of each of theindividual layers, respectively, of the thin film stack.

Although a thin film stack may include multiple layers of differentmaterials, in practice, a thin film stack is usually comprised of alayer of thin film on top of a comparatively thicker substrate forsupporting the thin film. In such a case, the thermal equilibration timeof a thin film stack is often dominated by the substrate. For example,for a thin film stack 190 composed of a thin film 191 located on top ofa substrate 192, as shown in FIG. 1, wherein thin film 191 has athickness x_(f) and a thermal equilibration time τ_(f), and substrate192 has a thickness x_(s) and a thermal equilibration time τ_(s), thetotal thermal equilibration time τ_(stack) of thin film stack 190 issimply the thermal equilibration time τ_(s) of substrate 192 whenx_(s)»x_(f).

The above-mentioned principle can be illustrated with a practicalexample. When substrate 192 is made of polyethylene terephathalate (PET)with c_(s)=730 J/kg-K, ρ_(s)=1.4 g/cm³, x_(s)=150 micron and κ_(s)=0.24W/m-K, and thin film 191 is made of silver with c_(f)=235 J/kg-K,ρ_(f)=10.5 g/cm³, x_(f)=1 micron and κ_(f)=420 W/m-K, the thermalequilibration time of substrate 192 (τ_(s)) and thin film 191 (τ_(f))are 24 ms and 1.5×10⁻⁶ ms, respectively. Thus, the thermal equilibrationtime of thin film stack 191 is nearly indistinguishable from that ofsubstrate 192 alone when x_(s)»x_(f).

B. Thermal Processing of a Thin Film Stack

When thermally processing thin film 191 on substrate 192, entire filmstack 190 can be heated to a maximum working temperature of substrate192 to minimize the thermal processing time. Importantly, it is evenpossible to heat thin film 191 on substrate 192 to a temperature farbeyond the maximum working temperature of substrate 192 without damagingsubstrate 192 when substrate 192 is heated quickly and cooled quickly.

In order to achieve a very short heating time along with a very fastcooling rate for substrate 192, a single light pulse 201 with a durationt_(p), as depicted in FIG. 2a , is can be used to heat both thin film191 and substrate 192 to a temperature T_(peak). Temperature T_(peak)can be higher than the maximum working temperature T_(max) of substrate192, as shown in FIG. 2b , because the side of substrate 192 adjacent tothin film 191 is only at temperature T_(peak) for a very short time suchthat substrate 192 does not have an opportunity to change its propertiessignificantly. In addition, thin film 191 is rapidly cooled viaconduction to substrate 192.

In conjunction with the physical properties and dimensions of thin film191 and substrate 192, both the heating time and cooling rate of thinfilm stack 190 are determined by the thermal profile of the light pulse(i.e., the shape of the light pulse).

In accordance with a preferred embodiment of the present invention,light pulse 201 of FIG. 2a can be delivered to substrate 192 in the formof a composite light pulse 202. Composite light pulse 202 is composed ofmultiple light pulses. When composite light pulse 202 having a correctthermal profile is utilized, substrate 192 can be heated to atemperature far beyond its maximum working temperature in order toachieve the shortest drying time. When drying thin film stack 190, thepulse length of composite light pulse 202 is preferably shorter than thethermal equilibration time τ_(stack) of thin film stack 190.

As shown in FIG. 2a , composite light pulse 202 includes multiplemicropulses to allow the temperature profile in a thin film stack, suchas thin film stack 190 from FIG. 1, to be customized for an optimalcure. In its simplest form, composite light pulse 202 includes uniformmicropulses. In this case, composite light pulse 202 can be shaped bysix different parameters: i. intensity (voltage), ii. composite pulselength, iii. average number of composite pulses that impinge on asubstrate in any given area on a thin film stack, iv. pulse repetitionfrequency, v. number of micropulses, and vi. duty cycle of micropulses.When the non-uniform micropulses are utilized, the pulse length anddelay of each individual micropulse can be specified.

With substrate 192 having a maximum working temperature T_(max) thinfilm 191 located on substrate 192 can be heated by composite light pulse202 from FIG. 2a to a temperature T_(peak) when the heating time is veryshort and the cooling rate is very fast. As shown in FIG. 2c , when thetemperature at the surface of substrate 192 briefly reaches T_(peak),and the temperature at the surface of substrate 192 quickly levels toless than the maximum working temperature T_(max). Also, substrate 192quickly reaches the thermal equilibrium after being heated by thecomposite light pulse.

The parameters of an optimal composite light pulse for processing of athin film can be determined experimentally. First, a damage threshold ona thin film stack from a single light pulse is ascertained by selectinga pulse length that is shorter than the thermal equilibration time ofthe thin film stack and exposing the thin film stack to a series ofsingle light pulses of increasing areal power density until some damageto the thin film stack is observed. The optimal thermal processing forthat single light pulse length is generally the power that is slightlyless than the damage threshold power. Since the damage mechanism isoften thermally driven, i.e., related to the amount of energy deposited,a shorter pulse length generally has a higher areal power densitythreshold. Additionally, when the thin film is absorbing the light,shorter pulse lengths generally preferentially heat the thin film overthe substrate that increases the energy efficiency of the process.However, in the case of a drying process or any thermal process thatgenerates gas, the damage threshold is also related to the rate at whichthe gas can escape without causing a local “explosion” in the thin filmstack. Thus, there is also fundamentally a maximum areal power densityindependent of pulse length, which means efficient thermal processingcannot be achieve by simply continuing to reduce the pulse length.

When the above-mentioned single light pulse is transformed into a burstof shorter pulses (i.e., micropulses) of the same total pulse length,the energy efficiency of a very short pulse can be realized whiledepositing adequate energy to process the thin film. This processing canbe done at an instantaneous power (e.g., the power during a micropulse)beyond the single pulse damage threshold without damaging the thin filmstack.

The optimization of a composite light pulse for thermal processing canbe further improved by using a software simulation, such as SimPulse™from NovaCentrix of Austin, Tex., to simulate the thermal response ofthe thin film stack due to the exposure from the composite light pulse.By inputting the thermo-physical properties of each layer in the thinfilm stack as well as the output from the flashlamp, the simulationsoftware can provide the temperature at every location within the thinfilm stack during and after exposure to the composite pulse. When thisis done, damage to the thin film stack can reveal physical mechanismswhich cause damage. This allows one to design an optimal composite pulseto avoid a particular damage mechanism. For example, when the damagemechanism is a temperature limitation within the thin film stack, suchas the gasification temperature of the substrate, one may process thethin film near, but not exceeding that particular temperature.Similarly, when drying a film which has multiple solvents, each solventmay boil at a particular temperature. Thus, optimal processing of thatthin film may include a composite pulse with multiple constanttemperature processing zones in which drying is first performed at alower constant temperature to evaporate the more volatile solventfollowed by processing at a higher constant temperature to evaporate theless volatile solvent.

Although a thin film can be processed at a significantly highertemperature than the maximum working temperature of the substrate forprocessing times shorter than the thermal equilibration time of the thinfilm stack, the temperature that the thin film stack attains afterthermal equilibrium still needs to be lower than the maximum workingtemperature of the substrate or there will be damage. Thus, the totalamount of energy that can be placed into the thin film stack cannotexceed the total energy needed to heat the thin film stack up to themaximum working temperature of the substrate. That number can bedetermined by calculating the total enthalpy of the thin film stackincluding any heat of vaporization of any solvent in the thin film.

A composite light pulse can also provide two different constantprocessing temperature zones on a thin film stack. For example, as shownin FIG. 2d , a composite light pulse includes multiple micropulsescapable of providing two different processing temperature zones, and thetiming (in μs) of the composite light pulse is listed in Table I.

TABLE I Turn on Turn off 0 87 193 238 473 508 763 793 1,063 1,093 1,2761,341 1,536 1,581 1,816 1,856FIG. 2e shows the temperature of a substrate versus time after thesubstrate has been irradiated by the composite light pulse from FIG. 2d.C. Apparatus for Drying a Thin Film on a Thin Film Stack

Referring now to FIG. 3, there is depicted a diagram of an apparatus fordrying thin films, in accordance with a preferred embodiment of thepresent invention. As shown, a drying apparatus 300 includes aconveyance system 310, a flashlamp controller 330 and a flashlamp head320 having a flashlamp 350. A low inductance cable 325 is connectedbetween flashlamp controller 330 and flashlamp head 320. Conveyancesystem 310 moves a thin film stack 340 past flashlamp head 320 whileflashlamp controller 330 provides shaped pulses of current to flashlamp350 using pulse width modulation (PWM) such that the shaped pulses aresynchronized to the conveyance speed of thin film stack 340 onconveyance system 310. Preferably, flashlamp 350 is a sealed flash lampfilled with gases such as xenon, krypton or argon. Flashlamp 350 canalso be a water-wall flashlamp, sometimes referred to as a DirectedPlasma Arc (DPA) lamp.

Flashlamp controller 330 includes a control computer 360. Controlcomputer 360 preferably includes a processing unit, input devices suchas a keyboard, a mouse, a touchscreen, etc., and output devices such asa monitor, as they are well-known to those skilled in the art.

In order to pulse-width modulate a pulse train of a given duration, eachindividual pulse need to be relatively short in order to provide pulseshaping. Furthermore, the pulses need to be more intense than a sourceproviding a single pulse since it is not turned on for a portion of thetime. Thus, drying apparatus 300 needs to be capable of providing pulselengths as short as 10 microseconds with peak power in excess of 100kW/cm². In addition, the PWM frequency for pulses can be as fast as 50kHz.

The shape of light pulses emitted from flashlamp 350 as well as thephysical properties and dimensions of a thin film and substrate canaffect the thermal gradient and the subsequent temperature at which thethin film can be dried while without damaging the substrate. Thus,drying apparatus 300 also includes multiple sensors (not shown) forcollecting various information from different parts of drying apparatus300 as well as the film and substrate on thin film stack 340. Thecollected information from various sensors and user inputs are fed backinto computer control system 360 in which thermal profiles can bere-calculated. Using the re-calculated thermal profiles, flashlampcontroller 330 controls the waveforms of the light being delivered tothin film stack 340 by flashlamp 350 while thin film stack 340 is beingconveyed under flashlamp 350.

With reference now to FIG. 4, there is depicted a block diagram offlashlamp controller 330. As shown, flashlamp controller 330 includes anencoder 510, an arbitrary waveform generator 520, a thermal simulator525, and control computer 360. A user initially inputs thin film stackproperties 540 and desired processing level 550 into flashlampcontroller 330. After receiving inputs, such as conveyance speed, fromconveyance system 310 (from FIG. 3) and additional system limits 570,encoder 510 provides trigger signals to computer that sends signals toarbitrary waveform generator 520 at appropriate times for curing thinfilms located on conveyance system 310. With the trigger signals,arbitrary waveform generator 520 is able to generate waveforms ofvarious shapes and timing based on user inputs 540 and 550. Arbitrarywaveform generator 520 sends waveform signals to flashlamp driver 530that amplifies the waveform signals for driving flashlamp 350 (from FIG.3).

The feedback information allows for continuous and real-timeadjustability of parameters, such as pulse energy, pulse duration, pulsewaveform, etc., when drying apparatus 300. All of the above-mentionedparameters can be altered under software and/or hardware control on amillisecond time frame with a resolution of 0.1%.

When thin film stack 340 is moving, and the flashlamp pulse frequency issynchronized to the conveyance speed, the frequency is given by:

$f = \frac{1.67 \times S \times O}{W}$where

-   -   f=flashlamp composite pulse rate [Hz]    -   S=conveyance speed [m/min]    -   O=overlap factor (i.e., the average number of composite pulses        received by substrate at any given point)    -   W=width of flashlamp 350 in the conveyance direction [cm]        For example, with a conveyance speed of 100 m/min, an overlap        factor of 4, and a curing head width of 7 cm, the pulse rate of        the strobe is 95.4 Hz. For faster conveyance speeds, this        relationship can be satisfied by increasing the width of        flashlamp 450 or adding additional flashlamps.

In order to achieve a uniform cure over a substrate area larger than thearea irradiated by flashlamp 350, flashlamp 350 is required tosynchronize the delivery of composite light pulses to the conveyance ofthe substrate. However, if the conveyance speed is so fast that thesubstrate moves significantly during the delivery of the composite lightpulse, then a uniform cure on the substrate is not possible.

In accordance with a preferred embodiment of the present invention, auniform cure on a moving substrate can be attained over an arbitrarilylong distance of thin film stack 340 if thin film stack 340 moves lessthan 10% of the width of flashlamp 350 in the conveyance directionduring the delivery of the composite light pulse. Expressed in equationform:t<60×W/Swhere

-   -   t=length of the composite pulse [ms]    -   W=width of flashlamp 350 in the conveyance direction [cm]    -   S=conveyance speed [m/min]        Table II shows maximum pulse length of composite pulse [ms] for        uniform curing versus conveyance speed and the width of light        pulses in the conveyance direction. The time in milliseconds        that composite pulse must be shorter than to attain uniform        processing in the conveyance direction.

TABLE II light pulse width speed [m/min] 7 cm 14 cm 28 cm 1 420 8401,680 10 42 84 168 100 4.2 8.4 16.8 1,000 0.42 0.84 1.68

EXAMPLE 1 Drying and Sintering of Nano-silver Ink on PET

Two samples of nano-silver ink on PET were prepared, each sample being a1 micron thick of nano-silver thin film printed on a 150 micron thickPET substrate. A first sample was dried in an oven at 150° C. for 5minutes to drive off solvent and exposed to a single light pulse of 1 msin duration at 1.6 kW/cm² at a webspeed of 10 m/min with an overlapfactor of 4 depositing 1.6 J/cm² of energy with each delivery of singlelight pulse for a total of 6.4 J/cm² energy deposited onto the substrateto sinter the silver.

Without being dried in the oven, the second sample was exposed to a 1 mslong composite light pulse comprised of 6 different micropulses ofdiffering pulse lengths and delays, and the timing (in μs) of thecomposite light pulse is shown in Table III.

TABLE III Turn on Turn off 0 100 289 374 439 474 604 644 789 829 9991,037

The intensity of the light pulses was increased to 4.7 kW/cm² so thatthe total amount of energy deposited was identical to the first sample.The material was processed at a webspeed of 10 m/min with a overlapfactor of 4 depositing 1.6 J/cm² with each light pulse for a total of6.4×1.6 J/cm² deposited onto the substrate to dry and sinter the silverin a single pass.

The implication of this type of processing is that more processing canbe done with less total energy than a conventional oven. In the case ofconventional oven processing, the entire substrate, the air around it,and the conventional oven surrounding the processing zone must be heatedto process the thin film.

The thermal response at the thin film as well as the back of thesubstrate for a single pulse neglecting the enthalpy absorbed by theevaporation of solvents is similar to the curve shown in FIG. 2b . Thethermal response from the composite light pulse at the thin film and atthe back of the substrate is similar to the curve shown in FIG. 2c . Acomparison of the curves from FIGS. 2b and 2c shows that the amount oftime the thin film is at an elevated temperature is significantly morefrom a composite light pulse from a single light pulse. Specifically,the amount of time the thin film spends at about 800° C. (see FIG. 2c )is approximately twice as much as that from a single light pulse (seeFIG. 2b ). As both cases use the same amount of radiant exposure, thistranslates into more thermal processing for the same amount of energydeposited. In sum, the same amount of thermal processing can be achievedwith less energy.

Note that this has a very different effect than a continuous train ofsmall, rapid light pulses. In that case, the timescale of heating wouldbe larger than the thermal equilibration timescale of the thin filmstack and would be similar to being heated by a conventional oven. Thus,the surface would not reach the peak temperatures achieved in thepresent invention without damaging the thin film stack. Consequently, itwould have a lower processing rate over the present invention.

Additionally, the composite light pulse has another significantadvantage in thermal processes that evolve gas such has drying orgas-evolving chemical reactions. Since the composite light pulseincludes multiple micropulses, the thin film being dried is allowed to“breathe,” i.e., release gas, between micropulses. This action preventsthe build up of gas in the thin film that would otherwise undergo acohesive failure due to the rapidly expanding gas.

EXAMPLE 2 Multi-Temperature Zone Processing Accounting for SolventEvaporation

The tunability of the pulse profile is particularly useful for dryingthin films where multiple distinct processes can be performed in asingle pass. In short, a thin film that contains solvent cannot beheated as rapidly as one which is already dried. That is, when solventis in the thin film, a high power will rapidly expand the solvent and“explode” the thin film, resulting in a cohesive failure. Ideally, onedesires to first remove the solvent at a lower power until it is removedfollowed by a higher power exposure to perform additional thermalprocessing such as sintering. FIG. 2d shows a representative thermalresponse profile of the film and substrate of example 1 from a compositepulse in which the first portion of the pulse maintains the temperatureat the surface of the thin film at about 700° C. for the first 1.2 ms,followed by a higher power exposure in order to maintain the thin film'stemperature at 1,000° C. for the remaining 0.5 ms. In this example, thesolvent evaporation occurs during the lower power processing zone andthe sintering occurs during the higher temperature processing zone.Thus, as opposed to ordinary zone processing in which a material isconveyed in a oven with different regions, or zones, with differenttemperatures. The present invention allows the same type of processingto be done in time and is thus termed “temporal zone processing.”

The same principle can be applied to a thin film containing multiplesolvents in which multiple heating zones can be formed to evaporate eachsolvent in order of decreasing volatility. In the system of Example 1,the pulse profile can be calculated by accounting for the total enthalpychange of the primary solvent components, silver ink pigment andsubstrate when exposed to 6.4 J/cm², assuming that the system isperfectly absorptive and no energy is lost to the surroundingenvironment, it is found that 4.4 J/cm² is required just to heat andevaporate the solvents. The remaining silver metal heats very quick toapproximately 1,000° C. requiring a total enthalpy change of 0.15 J/cm².During the time between the pulses the energy leaks into the substratecausing it to rise to an estimate 146° C. requiring and enthalpy changeof 1.85 J/cm². The total amount of energy required is approximately 6.4J/cm².

EXAMPLE 3 Prevention of Cohesive Failure in a Thin Film by Modulation ofGas Generation

An aqueous copper precursor ink was formulated comprising 10.0% wt.copper (II) oxide, 4.5% wt. copper (II) acetate in a base containingethylene glycol and glycerol. Traces were printed onto a 125 micronthick PET sheet using an Epson Stylus C88 ink jet printer. Upon curingwith a flashlamp, the copper oxide and copper acetate are reduced by theethylene glycol and glycerol to form a film of conductive copper metal.The reduction reaction generates a moderate amount of gas.

The printed film was cured using the method and apparatus of the presentinvention with the following conditions: voltage 250 V, composite lightpulse duration=1,050 microseconds, 4 micropulses with a duty cycle of0.6 (i.e., each micropulse was 175 microsecond long with a delay of 117μs between pulses), overlap factor=3, web speed=6.4 m/min. The sampleyield was 100% with an average sheet resistance of 3.7 Ω/□.

When the identical trace was cured with the same equipment, but withonly a single pulse, the gas evolution caused a cohesive failure of thetraces resulting in a sample yield of only 64%. The average sheetresistance was 5.2Ω/□. Changing any of the input variables resulted in aless conductive or poorer yield trace.

As has been described, the present invention provides a method forthermally processing a thin film on a moving substrate. The presentinvention allows the thin film to be at an elevated temperature for asignificantly longer period of time than the prior art. This is doneusing the same amount of radiant energy in the same amount of total timeso not damage occurs to the substrate.

While the invention has been particularly shown and described withreference to a preferred embodiment, it will be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention.

What is claimed is:
 1. A method comprising: conveying a thin film stackpast a flashlamp, wherein said thin film stack includes a thin filmlocated directly on a substrate, wherein said substrate is at leasttwice thicker than said thin film; and irradiating said thin film stackwith a modulated light pulse to thermally process said thin film,wherein said modulated light pulse yields a thermal profile having aplurality of temperature peaks at a temperature higher than a maximumworking temperature of said substrate, wherein said maximum workingtemperature is the highest temperature said substrate can handle whenheated in an oven without being damaged, wherein said thin film stackhas a total thermal equilibration time:τ=(√{square root over (τ₁)}+√{square root over (τ₂ )})² where andτ₁τ₂are thermal equilibrium time of said thin film and said substrate,respectively, wherein$\tau_{1} = \frac{c_{1}\rho_{1}x_{1}^{2}}{4\kappa_{1}}$ where c₁=specific heat of said thin film, ρ₁=mass density of said thin film,x₁=thickness of said thin>film, κ₁=thermal conductivity of said thinfilm, and $\tau_{2} = \frac{c_{2}\rho_{2}x_{2}^{2}}{4\kappa_{2}}$ wherec₂ specific heat of said substrate, ρ₂=mass density of said substrate,x₂=thickness of said substrate, κ₂=thermal conductivity of saidsubstrate.
 2. The method of claim 1, wherein said conveying furtherincludes conveying said thin film stack less than 10% of the length of airradiating area of said flashlamp in a conveyance direction during thetime said modulated light pulse is being delivered.
 3. The method ofclaim 1, wherein a total time duration t_(p) of said modulated lightpulse is shorter than said total thermal equilibration time of said thinfilm stack.
 4. The method of claim 1, wherein said plurality oftemperature peaks are at identical temperatures.
 5. The method of claim1, wherein said plurality of temperature peaks are at differenttemperatures.
 6. The method of claim 1, wherein said modulated lightpulse is shaped by voltage, pulse length and duty cycle to yield saidthermal profile.
 7. The method of claim 1, wherein said maximum workingtemperature of said substrate is less than 450 ° C.